Makes no sense. How did Adobe get your credit/bank card details if you didn't give it to them when you joined?
If you're certain you or a family member never ordered / downloaded anything, then contact your bank immediately. Your card may have been compromised. If so, the bank will have you sign some legal papers before launching a fraud investigation with law enforcement and cancelling your card to further purchases.
Nancy O'Shea, Product User & Community Expert Alt-Web Design & Publishing ~ Web : Print : Graphics : Media